If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.

Intersections

Stage: 4 and 5 Challenge Level:

In this case, rather than working with the awkward numbers, you may
find it easier to substitute $\alpha = 0.99999$ and solve the
equations algebraically, and finally substitute $0.99999$ for
$\alpha$ to find the numerical solutions.

To explain the solutions think about the geometry associated with
these equations.

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NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.